Entropy and the time evolution of macroscopic systems:
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the follow...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Oxford Univ. Press
2008
|
| Series: | International series of monographs on physics
141 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the following 100 years, is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship with probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-twentieth Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy. |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 209 S. |
| ISBN: | 9780199546176 9780199655434 |
Staff View
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| 520 | |a This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the following 100 years, is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship with probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-twentieth Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy. | ||
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Record in the Search Index
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| adam_text | CONTENTS
Preface
xi
1
Introduction
1
A review of the origins of entropy and classical thermodynamics,
followed by a summary of 19th century attempts to explain these
theories in terms of the underlying molecular constituents of
macroscopic physical systems.
1.1
Heat
1
1.2
The emergence of entropy
3
1.3
Classical thermodynamics
5
1.4
Is there a deeper interpretation?
9
2
Some clarification from another direction
15
The origins of modern information theory are reviewed, along
with the early links with physics.
2.1
Information and physics
18
3
The probability connection
21
A brief introduction to probability as logic, and development of the
principle of maximum entropy as principally an algorithm of
probability theory for the construction of prior probabilities in the
presence of very general forms of information.
3.1
The principle of maximum entropy
26
4
Equilibrium statistical mechanics
and thermodynamics
34
An application of the theoretical tools developed in Chapter
3
to
macroscopic systems in thermal equilibrium, wherein the Gibbs
variational principle is understood as defining the equilibrium state.
4.1
The meaning of maximum entropy
43
4.2
Fluctuations
51
4.3
A mischaracterization
55
5
The presumed extensivity of entropy
59
The requirement that entropy be an extensive function of extensive
variables is examined in some detail, along with the possible
connection to the indistinguishability of elementary particles.
viii Contents
6
Nonequilibrium
states
69
The first extension of the maximum entropy principle to
nonequilibrium states is made here, with applications to
inhomogeneous systems. An initial contact with linear transport
processes in simple fluids is also included.
6.1
The linear approximation
72
6.2
Simple fluids
75
6.3
A transport example
79
6.4
Inhomogeneous systems
81
6.5
Some reflection
87
7
Steady-state processes
89
Application to nonequilibrium stationary processes is made at this
stage, with a focus on simple fluids.
7.1
Steady-state transport processes in simple fluids
93
8
Sources and time-dependent processes
99
A careful analysis of time evolution in macroscopic systems is
carried out, along with a critique of the standard equation of motion
for the density matrix. The practical difference between microscopic
and macroscopic equations of motion and the necessary relation to
external sources is recognized explicitly.
8.1
Equation of motion revisited
104
9
Thermal driving
107
The concept of thermal driving is introduced, wherein very general
external sources going beyond simple mechanical and electrical
forces are envisioned, from baseball bats to
Bunsen
burners.
Elements of nonequilibrium thermodynamics are presented.
9.1
Nonequilibrium thermodynamics
112
9.2
Linear heating
115
9.3
A special case: linear dynamic response
119
10
Application to fluid dynamics
124
An interlude in which the previous theoretical developments are
applied to the fluid dynamics of simple fluids and the derivation of
their macroscopic equations of motion from statistical mechanics.
10.1
Hydrodynamic fluctuations
126
10.2
Fluid dynamics equations of motion
128
10.3
The onset of turbulence
132
Contents ix
10.4 Ultrasonic
propagation
135
10.5
Correlations in nonequilibrium fluids
138
11 Irreversibility,
relaxation, and the approach
to equilibrium
142
Finally, the deep questions of the relation of entropy to these topics
first raised in Chapter
1
are addressed and resolved satisfactorily.
11.1
Irreversibility
143
11.2
The second law
148
11.3
Is time asymmetry an issue?
150
11.4
Relaxation and the approach to equilibrium
152
12
Entropy production and dissipation rates
160
The story concludes with a discussion of topics of current research
interest, with an emphasis on exposing various myths in the folklore.
12.1
The statistical mechanics formulation
167
Appendix A Perturbation theory
174
A mathematical exposition of the equations required to
describe small departures from equilibrium.
A.I Fluid equations of motion
178
A.
2
Operator identities
179
Appendix
В
Dissipative currents and Galilean
invariance
181
Microscopic expressions for dissipative currents in simple fluids are
exhibited, and the Galilean
invariance
of statistical mechanics is
discussed in some detail.
B.I Galilean
invariance
184
Appendix
С
Analytic continuation of covariance
functions
189
A brief discussion of how the covariance or correlation functions are
analytically continued into the complex plane so as to readily
analyze their casual and dissipative properties.
References
193
Name Index
205
Subject Index
207
|
| adam_txt |
CONTENTS
Preface
xi
1
Introduction
1
A review of the origins of entropy and classical thermodynamics,
followed by a summary of 19th century attempts to explain these
theories in terms of the underlying molecular constituents of
macroscopic physical systems.
1.1
Heat
1
1.2
The emergence of entropy
3
1.3
Classical thermodynamics
5
1.4
Is there a deeper interpretation?
9
2
Some clarification from another direction
15
The origins of modern information theory are reviewed, along
with the early links with physics.
2.1
Information and physics
18
3
The probability connection
21
A brief introduction to probability as logic, and development of the
principle of maximum entropy as principally an algorithm of
probability theory for the construction of prior probabilities in the
presence of very general forms of information.
3.1
The principle of maximum entropy
26
4
Equilibrium statistical mechanics
and thermodynamics
34
An application of the theoretical tools developed in Chapter
3
to
macroscopic systems in thermal equilibrium, wherein the Gibbs
variational principle is understood as defining the equilibrium state.
4.1
The meaning of maximum entropy
43
4.2
Fluctuations
51
4.3
A mischaracterization
55
5
The presumed extensivity of entropy
59
The requirement that entropy be an extensive function of extensive
variables is examined in some detail, along with the possible
connection to the indistinguishability of elementary particles.
viii Contents
6
Nonequilibrium
states
69
The first extension of the maximum entropy principle to
nonequilibrium states is made here, with applications to
inhomogeneous systems. An initial contact with linear transport
processes in simple fluids is also included.
6.1
The linear approximation
72
6.2
Simple fluids
75
6.3
A transport example
79
6.4
Inhomogeneous systems
81
6.5
Some reflection
87
7
Steady-state processes
89
Application to nonequilibrium stationary processes is made at this
stage, with a focus on simple fluids.
7.1
Steady-state transport processes in simple fluids
93
8
Sources and time-dependent processes
99
A careful analysis of time evolution in macroscopic systems is
carried out, along with a critique of the standard equation of motion
for the density matrix. The practical difference between microscopic
and macroscopic equations of motion and the necessary relation to
external sources is recognized explicitly.
8.1
Equation of motion revisited
104
9
Thermal driving
107
The concept of thermal driving is introduced, wherein very general
external sources going beyond simple mechanical and electrical
forces are envisioned, from baseball bats to
Bunsen
burners.
Elements of nonequilibrium thermodynamics are presented.
9.1
Nonequilibrium thermodynamics
112
9.2
Linear heating
115
9.3
A special case: linear dynamic response
119
10
Application to fluid dynamics
124
An interlude in which the previous theoretical developments are
applied to the fluid dynamics of simple fluids and the derivation of
their macroscopic equations of motion from statistical mechanics.
10.1
Hydrodynamic fluctuations
126
10.2
Fluid dynamics equations of motion
128
10.3
The onset of turbulence
132
Contents ix
10.4 Ultrasonic
propagation
135
10.5
Correlations in nonequilibrium fluids
138
11 Irreversibility,
relaxation, and the approach
to equilibrium
142
Finally, the deep questions of the relation of entropy to these topics
first raised in Chapter
1
are addressed and resolved satisfactorily.
11.1
Irreversibility
143
11.2
The second law
148
11.3
Is time asymmetry an issue?
150
11.4
Relaxation and the approach to equilibrium
152
12
Entropy production and dissipation rates
160
The story concludes with a discussion of topics of current research
interest, with an emphasis on exposing various myths in the folklore.
12.1
The statistical mechanics formulation
167
Appendix A Perturbation theory
174
A mathematical exposition of the equations required to
describe small departures from equilibrium.
A.I Fluid equations of motion
178
A.
2
Operator identities
179
Appendix
В
Dissipative currents and Galilean
invariance
181
Microscopic expressions for dissipative currents in simple fluids are
exhibited, and the Galilean
invariance
of statistical mechanics is
discussed in some detail.
B.I Galilean
invariance
184
Appendix
С
Analytic continuation of covariance
functions
189
A brief discussion of how the covariance or correlation functions are
analytically continued into the complex plane so as to readily
analyze their casual and dissipative properties.
References
193
Name Index
205
Subject Index
207 |
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| id | DE-604.BV023334930 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:59:12Z |
| indexdate | 2024-07-09T21:16:13Z |
| institution | BVB |
| isbn | 9780199546176 9780199655434 |
| language | English |
| lccn | 2008000550 |
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| physical | XIII, 209 S. |
| publishDate | 2008 |
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| publisher | Oxford Univ. Press |
| record_format | marc |
| series | International series of monographs on physics |
| series2 | International series of monographs on physics |
| spelling | Grandy, Walter T. 1933- Verfasser (DE-588)133917053 aut Entropy and the time evolution of macroscopic systems Walter T. Grandy New York [u.a.] Oxford Univ. Press 2008 XIII, 209 S. txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 141 Hier auch später erschienene, unveränderte Nachdrucke This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the following 100 years, is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship with probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-twentieth Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy. Entropy (Information theory) Entropy - Statistical methods Entropy Statistical methods Entropie (DE-588)4014894-4 gnd rswk-swf Entropie (DE-588)4014894-4 s DE-604 International series of monographs on physics 141 (DE-604)BV000106406 141 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016518813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grandy, Walter T. 1933- Entropy and the time evolution of macroscopic systems International series of monographs on physics Entropy (Information theory) Entropy - Statistical methods Entropy Statistical methods Entropie (DE-588)4014894-4 gnd |
| subject_GND | (DE-588)4014894-4 |
| title | Entropy and the time evolution of macroscopic systems |
| title_auth | Entropy and the time evolution of macroscopic systems |
| title_exact_search | Entropy and the time evolution of macroscopic systems |
| title_exact_search_txtP | Entropy and the time evolution of macroscopic systems |
| title_full | Entropy and the time evolution of macroscopic systems Walter T. Grandy |
| title_fullStr | Entropy and the time evolution of macroscopic systems Walter T. Grandy |
| title_full_unstemmed | Entropy and the time evolution of macroscopic systems Walter T. Grandy |
| title_short | Entropy and the time evolution of macroscopic systems |
| title_sort | entropy and the time evolution of macroscopic systems |
| topic | Entropy (Information theory) Entropy - Statistical methods Entropy Statistical methods Entropie (DE-588)4014894-4 gnd |
| topic_facet | Entropy (Information theory) Entropy - Statistical methods Entropy Statistical methods Entropie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016518813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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